Physics — HSSC-II Practice Quiz

Gravitational field strength g at a point is the gravitational force experienced per unit mass placed at that point. Formula: g = GM/r² (= F/m). SI unit: N kg⁻¹ (or m s⁻²). It is a vector directed toward the mass producing the field.

Since g = GM/r², g depends on r (distance from Earth's centre ≈ 6.4×10⁶ m). For small heights h ≪ R, the change r = R + h is negligible compared with R, so g changes by an insignificant amount and may be treated as constant near the surface.

A satellite whose orbital period equals the Earth's rotational period (≈ 24 hours), orbiting from west to east directly above the Equator. It therefore stays fixed above the same point on Earth — used for communication and weather monitoring. Its orbital radius is about 4.23×10⁷ m.

Gas molecules move randomly and continuously collide with the walls of the container. At each collision a molecule's momentum changes, exerting a force on the wall. The total force per unit area from these countless collisions is the pressure of the gas.

From kinetic theory, pV = ⅓Nm⟨c²⟩ and average translational KE = ½m⟨c²⟩. Combining gives pV = ⅔N(½m⟨c²⟩), i.e. pressure is directly proportional to the average translational kinetic energy (and hence to absolute temperature) of the molecules.

Because real gas molecules (i) have intermolecular forces of attraction and (ii) occupy a finite volume — both ignored in the ideal model. Deviations become large at high pressure and low temperature, where molecules are close together.

Simple harmonic motion is a to-and-fro motion in which the acceleration is directly proportional to the displacement from a fixed (mean) point and is always directed towards that point: a = −ω²x. The restoring force is proportional to displacement (F = −kx).

Total energy ½mω²x₀² stays constant. At the mean position KE is maximum and PE is zero; at the extreme positions PE is maximum and KE is zero. Energy continuously converts KE ⇌ PE while the sum remains fixed.

(i) Tuning a radio/TV to a station (electrical resonance). (ii) Heating food in a microwave oven. (iii) Pushing a swing at its natural frequency. (Also: shattering a glass by sound, vibration of a bridge.)

Free oscillation: a system displaced and released vibrates at its own natural frequency, e.g. a struck tuning fork or a simple pendulum. Forced oscillation: a system driven by an external periodic force, e.g. a vibrating bridge under marching feet or a loudspeaker cone driven by AC.

(i) The two sources must be coherent (constant phase difference). (ii) They must have the same frequency/wavelength and nearly equal amplitude. (iii) The sources must be close together and the screen far away (and waves of the same polarization).

An optical device consisting of a very large number of equally spaced, close parallel slits (lines) per unit length. It diffracts light into sharp, widely separated maxima and is used to determine the wavelength of light using d sin θ = nλ.

Constructive: path difference = nλ (n = 0,1,2,…) — waves in phase, bright fringe. Destructive: path difference = (n + ½)λ — waves out of phase, dark fringe.

Electric potential at a point is the work done per unit positive charge in bringing a small test charge from infinity to that point. For a point charge: V = q / (4πε₀r). SI unit: volt (J C⁻¹).

Used in flash guns of cameras, electric fans (starting capacitor), refrigerators, and in rectification/smoothing circuits of power supplies — to store charge and release it quickly or to smooth current.

In series the charge Q on each is the same; voltages add: V = V₁ + V₂ = Q/C₁ + Q/C₂. Since V = Q/C, dividing by Q gives 1/C = 1/C₁ + 1/C₂. The combined capacitance is smaller than the smallest individual capacitor.

Self-inductance (L): the property of a coil that opposes any change of current in itself by inducing a back-emf. Mutual inductance (M): the emf induced in one coil due to a changing current in a neighbouring coil. SI unit of both: henry (H).

The peak value (I₀, V₀) is the maximum instantaneous value of the alternating quantity. The rms value is the steady DC value that produces the same heating effect: I = I₀/√2 and V = V₀/√2 for a sinusoidal AC.

The capacitor is connected across the load. It charges at the peaks and discharges slowly through the load between peaks, filling in the dips. This smooths the pulsating rectified output toward steady DC; larger C and load resistance give less ripple.

Here ω = 2×10³ rad s⁻¹ and C = 0.5×10⁻⁶ F. Capacitive reactance X_C = 1/(ωC) = 1 / (2×10³ × 0.5×10⁻⁶) = 1 / (10⁻³) = 1000 Ω (1 kΩ).

When electromagnetic radiation of frequency ≥ the threshold frequency strikes a metal, each photon (energy hf) gives its energy to one electron. If hf exceeds the work function ϕ, the electron escapes as a photoelectron with KE = hf − ϕ.

It is impossible to measure both the position and momentum of a particle simultaneously with perfect accuracy. The product of the uncertainties is at least of the order of h: Δx · Δp ≥ h/4π. (If Δx → 0, then Δp → ∞.)

Resolution is limited by wavelength. Fast electrons have a very small de Broglie wavelength (λ = h/p) — far shorter than visible light — so an electron microscope can resolve much finer detail than an optical microscope.

A photon has zero rest mass but carries momentum p = E/c = h/λ, so light can exert a force (radiation pressure). For λ = 1 Å = 10⁻¹⁰ m: E = hc/λ = (6.63×10⁻³⁴ × 3×10⁸)/10⁻¹⁰ ≈ 1.99×10⁻¹⁵ J = ≈ 12.4×10³ eV.

Binding energy per nucleon rises steeply for light nuclei, peaks at ≈ 8.8 MeV around iron (A ≈ 56), then falls slowly for heavy nuclei. The peak means iron-group nuclei are most stable; fusion of light nuclei and fission of heavy nuclei both move toward this peak, releasing energy.

Mass defect: the difference between the total mass of the separate nucleons and the actual (smaller) mass of the nucleus. Binding energy: the energy equivalent of this mass defect (E = Δmc²) — the energy needed to break the nucleus into its nucleons.

Control rods (e.g. boron or cadmium) absorb excess neutrons. By inserting or withdrawing them, the rate of the fission chain reaction is controlled — pushed in to slow it down or pulled out to speed it up, keeping the reaction steady and safe.

The half-life (T½) is the time in which half the radioactive nuclei in a sample decay. It is constant for a given isotope. e.g. for an isotope of T½ = 8 days, 16 g decays to 8 g after 8 days, 4 g after 16 days, and so on. Related to decay constant by λ = 0.693/T½.

Luminosity is the total power of radiation emitted by a star in all directions (energy radiated per second). SI unit: watt (W). It depends on the star's surface area and temperature (L = 4πr²σT⁴).

Annihilation occurs when a particle meets its antiparticle (e.g. electron + positron). Their entire mass converts into energy, producing a pair of gamma-ray photons moving in opposite directions, conserving mass-energy and momentum.

It states that the total power radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature. For a star: L = 4πr²σT⁴, where σ is the Stefan–Boltzmann constant. A small rise in T greatly increases luminosity.

(a) Cryosphere: the part of Earth's climate system made of frozen water — ice sheets, glaciers, sea ice and permafrost. (b) Lithosphere: Earth's solid upper rocky layer (the surface land/crust) that interacts with the atmosphere and oceans.

Climate inertia is the phenomenon by which climate systems show resistance or slowness to change when a significant factor is altered. e.g. even if greenhouse emissions stabilise, the climate responds slowly because of complex feedback systems (oceans store heat for a long time).

Earth's climate is driven by the Earth energy budget — the balance between incoming solar radiation and outgoing radiation. Unequal heating between the equator and poles creates an energy imbalance that drives atmospheric circulation and ocean currents, shaping global climate.

A piezoelectric transducer uses the piezoelectric effect to both generate and detect ultrasound waves: an AC voltage makes the crystal vibrate (producing ultrasound), and returning echoes deform the crystal to produce a voltage — used for diagnostic ultrasound imaging.

X-rays pass through soft tissue but are absorbed by denser structures (bones, teeth), producing a contrast image of internal structures. They are used to detect fractures, tumours and other abnormalities inside the body.

A high-energy gamma photon (energy ≥ 1.02 MeV, i.e. ≥ 2m₀c²) must interact near a heavy nucleus (to conserve momentum). The photon then converts into an electron–positron pair, conserving charge, energy and momentum.

Force per unit mass at a point; g = GM/r²; unit N kg⁻¹. Directed toward the mass.

Peak = maximum instantaneous value; rms = I₀/√2 (same heating effect as equivalent DC).

Δx·Δp ≥ h/4π — position and momentum cannot both be known exactly.

Mass defect = (sum of nucleon masses − nuclear mass); binding energy = Δmc².

A piezoelectric transducer generates and detects ultrasound for diagnostic imaging.

Tuning a radio, microwave oven, pushing a swing at its natural frequency.